Advance Modeling of a Skid-Steering Mobile Robot for Remote ...

2.1 State of the Art 13and V = [v x v y ω z ] T , with v x , v y , ω z determining respectively the longitudinal, lateral andangular velocity of the vehicle.(a)(b)Figure 2.1: (a) SSMR kinematics; (b) Wheel/ground contact point velocities without slipping.By looking at Figure 2.1(a), it is easy to derive the following kinematic equation givingthe velocity constraint between the generalized velocity vector ˙q = [Ẋ Ẏ ˙θ] T 3 and thebody velocity vector V:⎡⎤cos(θ) − sin(θ) 0˙q = sin(θ) cos(θ) 0 V = g R l V (2.1)⎢⎣0 0 1⎥⎦where g R l is the rotation matrix projecting the local frame (x l , y l ) onto the inertial frame(X g , Y g ) in the case of planar motion.Let ICR G = (x ICRG , y ICRG , 0) denote the instantaneous center of rotation (ICR) of the entirerobot expressed on the local frame, which represents the point which the vehicle’s CoMrotates around. Accordingly to classical kinematics, in the condition of non longitudinalslipping, we can write the following equations:v = d C × ωv i = d i × ω(2.2)where v = [v x v y v z ] T and ω = [ω x ω y ω z ] T are respectively the linear and angular3 Note that the angular velocity on the inertial frame coincides to ˙θ because we are under the assumption of planar motion